6. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer
side is 30 metres more than the shorter side, find the sides of the field.
Answers
If the longer side is 30 metres more than the shorter side, find the sides of the field. Let the shorter side be x. Therefore, the diagonal = x + 60 & the longer side = x + 30. Since length can't be negative, therefore, the shorter side is 90m & the longer side is 120m.
Given:-
Long side of rectangular field is 60 meters more then the shorter side.
Let the longer side will be (y+30)mtr.
And the length of the diagonal will be (y+60) mtr.
Solution:-
Using Pythagoras theorem,
(Diagonal)² = (shorter side)² + (longer side)²
⇒(y+60)² = y² + (y+30)²
⇒y² + 3600 + 120y = y² + y²+900+60y
⇒3600+120y−y² −900−60y = 0
⇒−y² +60y+2700=0
⇒y² −60y−2700=0
⇒y² −(90−30)y−2700=0
⇒y² −90y+30y−2700=0
⇒y(y−90)+30(y−90)=0
⇒(y−90)(y+30)=0
If,
y+30=0
⇒ y=−30 (not possible)
If,
y−90=0
⇒y=90
So, the length of shorter side = y =60
Longer side 90+30=120
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